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Kinetic Theory of Solids. 537 



le( 4D D I 



d{e\e-E)~~ e 2 (e-Ey) 



{ 



2D J 1 4 



9E 4 (6 + 6') 2 6> 2 (6 + 6')6> 

 — 2 Jem 



l-4(6 + 6')0h . . . (11) 



9{b + b'y*0m/p 



whence, using the mean of the quasi-experimental values of k 

 given above as k l3 k 2 , k 3 , and the other known experimental 

 terms, we can get the values of b' for the metals. 



But our expression for the latent heat will be altered by 

 the variability of E. We have to find at what rate the 

 melting-pressure varies with the melting-temperature for a 

 collection of molecules that shrink with rising temperature. 

 Now melting has chiefly to do with the mobility of the indi- 

 vidual molecules. Each molecule of a solid, if it is not close 

 to the surface, moves as if it were free from the action of 

 molecular force, because the attractions of the molecules all 

 round it equilibrate one another. Let us conceive molecular 

 force not to exist, that is conceive a perfect gas compressed 

 till its molecules hem one another into fixed mean positions, 

 this will be identical with our solid; except that molecular 

 pressure is replaced by external pressure, the condition of the 

 individual molecules is the same. Now melting occurs when 

 the molecules escape from their domains, and suppose this 

 happens for values e, E, p, and 6 of the variables : it is desired 

 to find how much the temperature is to be raised to reach the 

 melting-point when p is increased to p + dp. It is obvious 

 that e/E must remain constant, and the only other condition 

 is that the collisional pressure increase must be equal to dp. 

 Hence, if in our equation we ignore the molecular-force term 

 and find dp/dd on the supposition that e/E is constant, 

 we can take it as dp/dO in the thermodynamic relation 

 \=6(v 2 -v 1 )dp/d0, 



But e/TZ = fJL say, and E is a function of 9 only, so that 

 de/d6=fidE/dd= -/*E Q b', 



.-. de/edO- ~6'E /E= -V(l -f I/O). 



Hence at the melting-point, 



3<?(e-E) 



^^^'■toh (12) 

 o{b + b)m/p v J 





